They could, but I'd be surprised if they do.

Firstly, we can see that they're using the email exactly as provided (for sending, at least), else filters on the mail we receive wouldn't work.

Secondly, the + trick works because it's valid in email addresses under RFC 5321 and RFC 5322 - the fact that Gmail (and others?) direct all addresses of the format 'foo+bar@gmail.com' to the mailbox of 'foo@gmail.com' is a quirk, not a given. Anyone wanting to trim '+bar' would have to know it's safe to do so for particular providers, and I doubt anyone wants to maintain that list and do extra backend work just in case they want to share on the sly.